Using Control Theory to Model the Long-term Economic Effects of Wildfire

Wildland fire management strategies often have long-term economic and ecological impacts, as evidenced by the increase in fire danger resulting from the total suppression policy of the last several decades. In the long run, the choice of an optimal wildland fire management strategy depends upon the cumulative effects of fire management factors as well as the interaction between them. A theoretical extension to the cost plus net value change (C+NVC) model is developed by using the principles of control theory. It explores the long-term relationships among the factors of production and the choice of optimal management strategies given that fire management actions have consequences in the future. Introduction The cost plus net value change (C+NVC) framework has been the most widely used economic fire management tool since its inception in 1916 (Headly). Although the model has evolved to account for changing management philosophy (Gorte and Gorte 1979, Pyne 1996), further adaptations will enable managers to meet the objectives of ecosystem management. Wildfire managers are broadening their focus from individual fires and annual budgeting concerns to include ecosystem-wide objectives and long-term effects. Such objectives include long-term cost efficiency, sustainability of fire programming, and the consideration of ecological effects (Williams and others 1993). These objectives are important aspects of ecosystem management and fire planning, yet are not adequately addressed by existing models. The C+NVC model minimizes the sum of fire management expenditures plus the net change in resource value for damaging wildfires. Total costs include annual expenditures on suppression and presuppression. Presuppression, or program level, is a combination of fire management activities (prevention, detection, and fuels management) that constitute the fire management mix (Mills and Bratten 1988). Once the program level has been defined, the optimal combination of presuppression activities is then determined (Gonázlez-Cabán and others 1986). Research to improve various components of the C+NVC model has included efforts to reduce program cost or to improve the efficiency of the fire management mix derived from the least cost program level. For example, Bellinger and others (1983) analyzed the cost effectiveness of resulting program levels and determined that the program cost was appropriate, yet efficiency could be improved by reallocating management mix activities. Similarly, González-Cabán and others (1986) used the C+NVC framework to demonstrate that an efficient management mix can be determined, given the optimum program level. Mills and Bratten (1982) developed the Forest Economics Evaluation System (FEES) to address cost effectiveness and efficiency of C+NVC based programs. Upon testing it (1988) they determined that the total program cost was almost solely a function of presuppression. Finally, Hesseln and others (1998) developed a theoretical extension to the C+NVC using catastrophe theory. They modeled the production function for wildfire behavior and subsequently related environmental and ecological effects to economic outcomes of wildland fire management (Hesseln and others 1999). These research efforts, however, do not consider the long run. An abbreviated version of this paper was presented at the Symposium on Fire Economics, Planning, and Policy: Bottom Lines, April 5-9, 1999, San Diego, California. Assistant Professor, School of Forestry, University of Mon­ tana, Missoula, MT 59812. e­ mail:[email protected] Professor, Forest Sciences, Colorado State Universi ty, Fort Collins, CO 80523. e-mail [email protected]. USDA Forest Service Gen. Tech. Rep. PSW-GTR-173. 1999. 107 Session III Using Control Theory to Model—Hesseln, Rideout Fire management activities often have profound long-term effects on the ecology of a region, and over time, affect how the landscape responds to wildfire (Wade and Lundsford 1990, Weber and Taylor 1992). Similarly, the effects of current fire management investments, such as fuels reduction, will likely be manifested in the future through reduced hazard of catastrophic fire and resultant ecological, physical, and financial damage. The C+NVC model, as it is currently used, does not embody the theoretical association between fire management programs and ecological effects elicited by those programs, and therefore, does not address long-term ecosystem management objectives. Furthermore, theoretical extensions of the model to address long-term sustainability of fire management programs-combinations of presuppression and suppression-have not been developed, thereby ignoring potentially important economic ramifications of various fire management activities. To better enable managers to address long-term economic objectives, we develop a theoretical extension to the C+NVC model by using control theory. Our objectives are to explore the long-term economic relationships among fire management activities and physical and financial damage, and to investigate the applicability of control theory to formulate a long-term optimization model. Our analysis is an extension of the C+NVC cusp model (Hesseln and others 1998, Hesseln and others 1999) that embodies environmental and ecological effects of fire behavior. We begin first with a review of the C+NVC model and then discuss the principles of control theory in the context of fire management modeling. Finally, we conclude with a discussion of long-term fire management planning. Evolution of the C+NVC Model The C+NVC model was developed to minimize the sum of fire management expenditures plus the net change in resource value resulting from wildfire. The relationship between fire management expenditures and net value change is specified by equation [1]: C + NVC = WS + WP + NVC(S,P) [1] in which cost C is the sum of suppression and presuppression expenditures S and P evaluated at their prices W and W. The net change in resource value NVC is a function of management activities S and P (fig. 1).